Problem: Simplify the following expression and state the condition under which the simplification is valid: $z = \dfrac{n^2 + 3n}{n^2 - 7n - 30}$
Answer: First factor the expressions in the numerator and denominator. $ \dfrac{n^2 + 3n}{n^2 - 7n - 30} = \dfrac{(n)(n + 3)}{(n - 10)(n + 3)} $ Notice that the term $(n + 3)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(n + 3)$ gives: $z = \dfrac{n}{n - 10}$ Since we divided by $(n + 3)$, $n \neq -3$. $z = \dfrac{n}{n - 10}; \space n \neq -3$